[...]
> Well, suppose WebOnt fixed the layering issue, perhaps by using an
approach
> with explicit comprehension principles that did not have paradoxes.
> (Remember, however, that there are several people who believe that this
is
> probably not possible, and there is no proponent for this approach.) It
> still would be possible to have a too-weak solution. For example, Jos
has
> been producing log:implies stuff that are, in a sense, like the
> comprehension principles. As far as I can remember, every set of
> implications that he has produced has been shown to be too weak, in the
> sense that there are desirable consequences that do not follow from the
> rules.
1) there is one thing I would like to reiterate
suppose we have a paradoxical pair such as e.g.
{ ?x a :R } log:implies { ?x a [ owl:complementOf ?x ] } .
{ ?x a [ owl:complementOf ?x ] } log:implies { ?x a :R } .
then deriving a contradiction from that is indeed a
VALID inference but it is not a SOUND inference and
I think we should aim for sound reasoners giving
sound arguments (an argument is sound if and only if
it is valid and all its premises are true).
2) yes, more desirable consequences should follow
from more implications, but also there should
be more rules for deriving inconsistencies
such as e.g.
{ :rule16r1 .
?s ?p ?o .
?s a [ a owl:Restriction;
owl:onProperty ?p;
owl:minCardinality ?min;
owl:maxCardinality ?max;
owl:toClass ?C ] .
{ ?s ?p ?o . ?o a ?C } math:entailCount ?n .
?n math:lessThan ?min
}
log:implies
{ ?s :inconsistentWith owl:Restriction } .
where math:entailCount is just something to count
how many times we can entail its subject graph
from what was given
--
Jos